A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

Chapter 6

Solution of Linear Systems

Chen Greif

Very often, the primary computational bottleneck in the solution

of a problem in applied geometry and other areas of applications

is the numerical solution of one or several linear systems that arise

throughout the computation:

Ax = b,

where A ∈ R

n×n

and x, b ∈ R

n

. Even a modest understanding

of the properties of the underlying matrix may help in making a

good choice of a solution method.

If A is non-singular, the above linear system has a unique solu-

tion for any given right-hand side vector b. Numerical methods for

solving linear systems of equations can generally be divided into

two classes: direct metho ...